Trace-anomaly decomposition and universal dark matter scaling in compact stars

Abstract

We investigate how dark matter (DM) admixture modifies the conformal properties and phase structure of dense neutron-star matter within a self-consistent single-fluid framework, with the global DM fraction $F_{\chi }=N_{\chi }/N_B$ fixing the local relation $n_{\chi }=F_{\chi }{n}_B$. We derive an exact decomposition of the total trace anomaly, ${\Delta }_{\mathrm{tot}}$, into microscopic contributions. For collider-motivated Higgs-portal benchmarks, explicit Higgs, vector-mediator, and contact-interaction contributions are negligible, while heavy nonrelativistic DM has an intrinsic trace anomaly close to the nonrelativistic limit, ${\Delta }_{\chi }\simeq 1/3$. Consequently, the DM rest-mass energy fraction dominates the DM-induced modification of ${\Delta }_{\mathrm{tot}}$, producing a smooth upward shift of up to $\sim 0.1$ for $F_{\chi }\sim 0.2\%$. In the pressureless, comoving heavy-WIMP regime, we further identify a universal dark-sector scaling governed by the mass-loading parameter $\lambda =F_{\chi }{m}_{\chi }/m_N$: numerical calculations with different $(F_{\chi },m_{\chi })$ pairs at fixed $\lambda$ exhibit overlapping trace-anomaly, sound-speed, and mass--radius responses for a given baryonic equation of state. In hybrid stars, DM leaves the coexistence pressure and chemical potential essentially unchanged, whereas first-order hadron--quark deconfinement produces sharp discontinuities in the squared sound speed $c_s^2$, ${\Delta }_{\mathrm{tot}}$, and ${\Delta }_{\mathrm{tot}}-{\Delta }_B$. The combined softening substantially reduces the maximum stellar mass, placing $F_{\chi }\sim 0.2\%$ in tension with the observed $2M_{\odot }$ neutron stars. These results show that the trace anomaly and its density evolution provide a sensitive diagnostic for distinguishing smooth DM-induced modifications of dense matter from genuine first-order deconfinement.

Comments: 13 pages, 5 figures, and 2 tables